Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500's [Dur77], but have not been studied extensively until recently. Over the past few years, there has been a surge of interest in these problems in discrete and computational geometry. This paper gives a brief survey of some of the recent work in this area, subdivided into three sections based on the type of object being folded: linkages, paper, or polyhedra. See also [O'R98] for a related survey from this conference two years ago. In general, we are interested in how objects (such as linkages, paper, and polyhedra) can be moved or reconfigured (folded) subject to certain constraints depending on the type of object and the problem of interest. Typically the process of unfolding approaches a more basic shape, whereas folding complicates the shape. We can also generally define the configuration space as the set of all configurations or states of the object, with paths in the space corresponding to motions (foldings) of the object.
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